Although some sources state that Carol Haney and Eydie Gormé both turned down the role of Rose before it was somewhat reconceived and offered to Chita Rivera, the truth may be a bit more complex. Charles Strouse has discussed several times what happened Haney. One time was in an interview posted at Rob Weiner-Kendt's blog The Wicked Stage.
Rob Weiner-Kendt: I heard a story that Carol Haney was originally going to play the part of Rosie, later played by Chita Rivera, and that her character was originally Polish. So was there a song called "Polish Rose" that you had to change to "Spanish Rose"?
Charles Strouse: It was more than a song. Originally, when the story was written by Lee [Adams] and Mike [Stewart] and me, the girl, Rosie, was Polish, and every joke that the mother made was about Poles, which actually was kind of fashionably unfashionable then—there were all kinds of dumb Polish jokes. And Carol got sick. She was kind of a bad-luck girl—a wonderful performer who had a certain lack of stability in her life. The first day that Lee and Gower Champion and Mike came down to her apartment to hear her sing—I had taught her about four songs—she suddenly lost her voice. And we all sat around for about a half-hour, until it became embarrassing, because everybody knew there was a problem we couldn't possibly touch at that moment. I remember Gower saying "We'll talk later," and we all knew it wasn't going to happen.
As for Eydie Gormé, she became pregnant, effectively ending her availability.